I'm unaware of any protests during the war about firebombing Tokyo, which BTW killed more people that Hiroshima and Nagasaki combined.
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If you look at contemporary accounts in magazines like "Time" and "Life" you will see that these raids were invariably presented as attacks on dispersed war production sites and so forth. The firebombing of Tokyo, just like the RAF firebombings of Hamburg, etc., could be portayed as attacks on the infrastructure necessary to prolong the enemys' war effort (including worker residences) because bombs either blow stuff up or burn it. You're correct that in the popular mind, German and Japanese civilians had it coming so the massive loss of life was no big deal. But there is a difference when you gas people and give them diseases. It's plainly obviously at that point that your sole aim is killing people and the allies consistently tried to portray themselves in their internal and external propaganda as better than that (so did the Germans for that matter, but that's another story). I'd argue that massed chemical and biological attacks on Japanese cities would ultimately provoke far more revulsion than the atomic bombs. A-bombs blow stuff up and destroy factories...and Hiroshima was referred to as a major industrial center.
You are right, there were no protests about the bombings in the modern sense of "protest". I am aware, however, that people did write "letters to the editor" carefully expressing some moral concerns about city bombing and similar joint letters were sent from universites, etc.